# Tag Info

Accepted

### What, in simplest terms, is gauge invariance?

The reason that it's so hard to understand what physicists mean when they talk about "gauge freedom" is that there are at least four inequivalent definitions that I've seen used: Definition 1: A ...
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### What role does "spontaneous symmetry breaking" play in the "Higgs Mechanism"?

It is frequently stated the Higgs mechanism involves spontaneous breaking of the gauge symmetry. This is, however, entirely wrong. In fact, gauge symmetries cannot be spontaneously broken. A ...
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### If Energy can be converted into mass, why can it not be converted into charge?

You're making some category errors in the question. Energy can't be converted into mass, mass is a form that energy can take. In other words, when energy is "converted" into mass it never stops being ...
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### Physical difference between gauge symmetries and global symmetries

The first answer to such a question must always be: A gauge symmetry has no "physical" meaning, it is an artifact of our choice for the coordinates/fields with which we describe the system (cf. Gauge ...
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### What role does "spontaneous symmetry breaking" play in the "Higgs Mechanism"?

In short: The spontaneous breaking of global U(1) symmetry, rather than local 'gauge symmetry', gives rise to the non-zero vacuum expectation value of Higgs field. This non-zero VEV is an essential ...

### What, in simplest terms, is gauge invariance?

I only understood this after taking a class in general relativity (GR), differential geometry and quantum field theory (QFT). The essence is just a change of coordinates systems that needs to be ...
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### Covariance in gauge theories: why should the Lagrangian be gauge invariant

We do not start from the assumption that the Lagrangian "should" be invariant under gauge transformations. This assumption is often made because global symmetries are seen as more natural than local ...
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### How do symmetries “define” physical laws?

A theory is typically described by a Lagrangian, and varying this gives us the equations of motion of the system. The symmetries you describe are symmetries of the Lagrangian i.e. they are ...
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### What is $U(1)$ symmetry?

Let us first refer to symmetry generically. When we say a theory is symmetric under $G$ ($G$ some group) we mean that the elements of $G$ transform the states, and the operators of a theory, (in the ...
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### What, in simplest terms, is gauge invariance?

Since you mentioned coming from a mathematics background, you might find it nice to take an answer in terms of equivalence classes. A gauge theory is physical theory where the observable quantities, ...
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### What defines a large gauge transformation, really?

Bundles and compactified spacetime A gauge theory cannot be looked at purely locally, it has inherently global features one cannot see locally. The proper mathematical formalization of a Yang-Mills ...
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### Diffeomorphism group vs. $GL(4,\mathbb{R})$ in General Relativity

Let there be given a 4-dimensional real manifold$^1$ $M$. As OP says, the set ${\rm Diff}(M)$ is the group of globally defined $C^{\infty}$-diffeomorphisms $f:M\to M$. The set ${\rm Diff}(M)$ is an ...
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### What, in simplest terms, is gauge invariance?

Here's the most elementary example of a gauge symmetry I can think of. Suppose you want to discuss some ants walking around on a Möbius band. To describe the positions of the ants, it's convenient to ...
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• 123k
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### How is the Chern-Simons action well-defined?

The expression of the Chern-Simons functional as an integral over a 3-apace is just a shorthand notation. The integration in the Chern-Simons functional differs from the integration of differential ...
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